How to Flip Rotation from Positive to Negative?
You have a few options. For all methods, orientate the bones as such, that the most important rotation is mirrored by default. In my case I made the X rotation control the in-out-movement.

1. Don't change anything

Blender features a mirrored copy-paste functionality. Select the left bone and press &#9096; CtrlC, then press &#9096; Ctrl&#8679; ShiftV. The copied pose will be pasted mirrored. These functions are also available as small buttons on the right of the header in pose mode.



When creating good/solid shapes for animation, a  symmetrical pose is seldom desired anyway. The animator will have to manipulate both brows anyways.

2. Add a parent control bone

Add an additional bone in the center, with which the animator can manipulate both brows at once. If he wants to manipulate either bone individually, this is also possible by selecting them directly.



This has no drawbacks from the first method, since both brows are transformable individually. To set this up, add a parent bone to each brow and a Brows bone in the center. (Hide the parent bones at the end.) Then add Constraints, transfering the transformation of the centered Brows bone to parent bones. I used a copy rotation constraint for one Axis (Z) and a Transformation constraint for the other axes, transfering the translation to rotation.

The transfer has to be inversed (mirrored) for two axes.



3. Scale the parent bone

This method achieves mirrored behaviour of two axes. Add a parent bone to both brows and a child bone. The child bone will be the deforming bone for this method. Since the X axis already mirrores, we can now add a second axis to be mirrored; I choose Z. To mirror Z, scale the Parent and the new Child (Deform) bone to -1 on Z.



X and Z will be mirrored. Add a driver to the scaled bones and hide them, just to make sure the inverse scale is never cleared.

4. Use inversed constraints for the deforming bones.

Add a deforming bone to each side, which is located at the same location and orientation as the brow. For one side, transfer the rotation from Brow control bone to deform bone with a copy rotation constraint. On the other side, do the same, but inverse the desired axes (in my case Y and Z). For the inversing side, select the Brow control bone and set its Custom Shape to display At the deforming bone.



Manipulating this bone will now display the Widget in a mirrored rotation, it may feel unnatural though.



Methods 2 - 4 are distributed on the first layers of this blend.